The one-term distributive homology was introduced by J.H.Przytycki as an
atomic replacement of rack and quandle homology, which was first introduced and
developed by R.Fenn, C.Rourke and B.Sanderson, and J.S.Carter, S.Kamada and
M.Saito. This homology was initially suspected to be torsion-free, but we show
in this paper that the one-term homology of a finite spindle can have torsion.
We carefully analyze spindles of block decomposition of type (n,1) and
introduce various techniques to compute their homology precisely. In addition,
we show that any finite group can appear as the torsion subgroup of the first
homology of some finite spindle. Finally, we show that if a shelf satisfies a
certain, rather general, condition then the one-term homology is trivial.Comment: 17 pages, 2 PS-Tricks figure
